Mathematics Item Sampler Grade 4 - dpi.wi.gov · PDF fileGrade 4 Mathematics Item Sampler iv ... This document contains samples of test items similar to those on the Wisconsin Forward

MathematicsItem Sampler

Grade 4

Grade 4 Mathematics Item Sampler ii

Developed and published under contract with the Wisconsin Department of Public Instruction by Data Recognition Corporation, 13490 Bass Lake Road, Maple Grove, MN 55311. Copyright © 2017 by the Wisconsin Department of Public Instruction. All rights reserved. Only State of Wisconsin educators and citizens may copy, download, and/or print the document, located online at https://dpi.wi.gov/assessment/forward/sample-items. Any other use or reproduction of this document, in whole or in part, requires written permission of the Wisconsin Department of Public Instruction.

The Wisconsin Department of Public Instruction does not discriminate on the basis of sex, race, color, religion, creed, age, national origin, ancestry, pregnancy, marital status or parental status, sexual orientation, or disability.

https://dpi.wi.gov/assessment/forward/sample-items

iiiGrade 4 Mathematics Item Sampler

MATHEMATICS ITEM SAMPLER OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Connection to the Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1How Do I Use This Book? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Professional Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Improving Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Student Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Test Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Depth of Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Item Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Selected-Response (SR) Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Technology-Enhanced (TE) Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Text-Dependent Analysis (TDA) Items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

MATHEMATICS ITEMS—SESSION 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

MATHEMATICS ITEMS—SESSION 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

MATHEMATICS—APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Summary Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

TABLE OF CONTENTS

Grade 4 Mathematics Item Sampler iv

THIS PAGE IS INTENTIONALLY BLANK.

1Grade 4 Mathematics Item Sampler

MATHEMATICS ITEM SAMPLER OVERVIEW

OVERVIEW

This document contains samples of test items similar to those on the Wisconsin Forward Mathematics Exam. Each sample test item has been through a rigorous review process by DRC, Wisconsin Educators, and a third party, to ensure alignment with the Wisconsin Academic Standards. These items will not be used on the state assessment and may, therefore, be used in Wisconsin for professional development and student practice. The items in this document illustrate a sample of the content and types of items that students will encounter on the Forward Exam. A Summary Data table in the Appendix section identifies the alignment (standard measured), answer key, depth of knowledge, and annotations for each item.

CONNECTION TO THE STANDARDS

Wisconsin Academic Standards for Mathematics are available on the DPI webpage. Test items require students to prove their knowledge and abilities as stated in the standards.

HOW DO I USE THIS BOOK?

Professional Development

Sample items are useful as educators engage in conversations about what students are expected to know and be able to do to demonstrate proficiency on the state assessments relative to the Wisconsin Academic Standards. Sample items can inform discussions about state and local standards, curriculum, instruction, and assessment.

Improving Instruction

Teachers may use sample items in classroom activities that help students understand how to

• review key vocabulary;

• solve problems;

• determine which answer choices are correct, which are incorrect, and why;

• approach long and/or multistep tasks;

• use good test-taking strategies.

Student Practice

Students may perform better and with less anxiety if they are familiar with the format of the test and with the types of items they will be required to answer. The Forward Exam is an online assessment; students will benefit from the use of the Online Tools Training in order to work within the system interface to answer items as they will appear on the assessment, as well as utilize the tools available to them in the online system.

Note: A student’s score on the practice test cannot be converted to a scale score, used to predict performance on the Forward Exam, or used to make inferences about the student’s learning.

https://dpi.wi.gov/standards

https://wbte.drcedirect.com/WI/portals/wi

Grade 4 Mathematics Item Sampler 2


Test Preparation

While using the Item Sampler for test preparation, care should be taken that this is done in a balanced manner and one that helps to enhance student knowledge of subject matter as well as test performance. Please note that test preparation is only useful to the extent that it is also teaching content area knowledge and skills. Therefore, the use of this resource for test preparation is of limited value to students due to the narrow opportunity for content learning. It is very important to ensure that teachers are teaching to the curriculum and not to the test, as teaching to the test narrows the focus of instruction to only that content covered by the test.



DEPTH OF KNOWLEDGEHess’ Cog

nitiv

e Rigo

r Matrix

& Curric

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pplying Web

b’s D

epth‐of‐K

nowledge Levels to

Bloom

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ITEM TYPES

The Wisconsin Forward Exam has multiple types of test items. However, because this item sampler is in a format that can be printed, the majority of its items are multiple-choice. In the Forward Exam, there will be a more diverse array of item types, including the ones described below.

Selected-Response (SR) Items

Selected-Response (SR) items are an efficient method for measuring a broad range of content, and can be used to assess a variety of skills. Three types of SR items are used on the online assessments: Multiple-Choice (MC), Enhanced Selected-Response (ESR), and Evidence-Based Selected-Response (EBSR). In all cases, SR items require that a student determines the correct answer(s) to the item posed from a provided list. While it is still possible for a student to perform some work directly related to determining the correct answer, the student is not required to generate the content of the answer when responding to a Selected-Response item. An exception to this requirement is Mathematics Short-Response/Gridded-Response items where students will be required to enter a short alphanumeric response.

Multiple-Choice (MC) Items

Multiple-Choice (MC) items on Wisconsin’s assessments have four answer choices, including three distractors and one correct answer. Distractors for Mathematics represent common misconceptions, incorrect logic, incorrect application of an algorithm, computational errors, etc. Distractors for English Language Arts (ELA) are written to represent a common misinterpretation, predisposition, unsound reasoning, casual reading, etc. A correct response to an MC item is worth one raw point. The process skills, directives, and action statements within an MC item also specifically align with the Wisconsin Academic Standards. Multiple-Choice items are present in all grades and are used with all content areas.

Multiple-Choice items can be further defined by being linked to, or independent from, a stimulus source. Items that operate independent of a stimulus are also known as “stand-alone MC.” Stand-alone items may still have tables, graphs, or other information used in support of the stem. English Language Arts uses a mixture of MC items linked to a stimulus passage and some that are stand-alone. For Mathematics, all MC items are considered stand-alone.

Enhanced Selected-Response (ESR) Items

The Enhanced Selected-Response (ESR) items are multi-part autoscored items that may consist of varying combinations of Multiple-Choice, Multiple-Response, Gridded-Response, Completion or Short-Answer, and Technology-Enhanced items that explore in greater depth and cognitive complexity the knowledge, skills, and abilities specified by the standards of each content area. Typically, this item type has a common focus and explores authentic problem-solving skills. An example of a Statistics and Probability Mathematics ESR item would utilize a data-table stimulus with Part A using a Technology-Enhanced (TE) graphing tool to create a bar graph of the data presented and Part B asking students to calculate the mean of the data using a Short-Response item.

Two-Part Evidence-Based Selected-Response (EBSR) Items

The Evidence-Based Selected-Response (EBSR) items have two parts and are designed to elicit a response based on what a student has read from a stimulus passage. EBSR items may be linked to a stimulus passage or to a stimulus passage set. There are several variations of two-part EBSR items, but all two-part EBSR items have an Accuracy piece and an Evidence piece.



The Accuracy piece of the item is Part A. Part A of a typical EBSR item will be similar to a standard MC test item. A student analyzes a passage and chooses a single, best (correct) answer from four answer choices. Part B of a typical EBSR item will elicit evidence from the stimulus passage and will require that the student selects one or more correct answers based on the response the student provided to Part A. Part B is also different from Part A in that it may have five or six answer options rather than just four answer options typical of an MC item and more than one option may be correct.

Technology-Enhanced (TE) Items

Technology-Enhanced (TE) item types share the same functional structure as traditional paper and pencil test items; however, the expansive features and functions of a computer-based medium allow for the incorporation of technical enhancements into traditional elements of a test item, such as the item stem, the stimulus (if any), the response area, or a combination of all three. TE items are used in the content areas of ELA, Mathematics, and Science.

Item types such as drag-and-drop, hot spot, and in-line selection of multiple answers from drop-down menus broaden item presentation with engaging, interactive open-ended items.

A wide variety of TE item types will be present on the Wisconsin Forward Exam, including, but not limited to:

• Clock Input, where a student is able to add an hour hand and a minute hand to the clock;

• Angle Draw Input, where given a base line, the student can represent an angle;

• Short Input, where there are many types of short inputs that can be used (The number of characters is usually limited to a relatively small number in order to facilitate auto-scoring. The types of characters allowed can also be limited to text only, numbers only, or a mix. An equation editor can be utilized to assist the student in creating something as basic as a fraction or something more complex. The available symbols and templates in the equation builder can be customized for a testing program. Certain Short Input items can also be used in a paper-based test (PBT) as a Gridded-Response item.);

• Bar Graph Input, where students can produce bar graphs with prepopulated titles, labels, and scales, or the system can allow the student to populate them (The number of bars and the color of the bars is predetermined by the system. A reset feature is available that allows the student to start over from the original configuration.);

• Number Line Input, where students can create a graph that might involve plotting points only or points and lines (Both solid and open “dots” are available as well as line segments and rays. Number line graphs can have prepopulated titles, labels, and scales or can allow the student to populate them.);

• Coordinate Graph Input, which allows for the graphing and labeling of points and lines (Regions, determined by plotted lines, can be shaded. Solid and open “dots” as well as solid and dashed lines are available to the student. Coordinate graphs can have prepopulated titles, labels, and scales or can allow the student to populate them.);

• Line Plot Input, which is used as another way to graphically represent data (The basic structure is provided for the student. Certain labeling on the line plot can be done by the student. A reset feature is available that allows the student to start over from the original configuration.);

• List Input, a combination of the short input described earlier that allows the student to add input boxes (For example, it can be used for describing the steps in a process without revealing to the student the number of steps needed. The added input boxes can be rearranged and/or deleted.);

• Drag-and-Drop Input, a wide variety of ways are available to utilize a drag-and-drop input (The main difference between it and a drag-and-paste is that each dragable entity can be used only once with a drag-and-drop input. A reset feature is available that allows the student to start over from the original configuration.);



• Drag-and-Paste Input, a wide variety of ways are available to utilize drag-and-paste input (The main difference between it and a drag-and-drop is that each dragable entity can be used more than once with a drag-and-paste input. A reset feature is available that allows the student to start over from the original configuration.);

• Drop-Down List Input, allows for the creation of a situation where a great deal of information about a student’s grasp of a concept can be determined with a single item (Students can be asked to choose from three function types, four number of real zero responses, and two inverse function responses. For one function alone, this provides 24 possible answer combinations. With the three functions, a considerable amount of information can be gained, making this almost an open-ended item type.);

• Pictograph using Drag-and-Paste, actually another example of drag-and-paste, but is worth mentioning on its own as it is a type of graphing often used at lower grade levels;

• Circle Graph, a graph that allows the student to create and label the “wedges” that represent the data (Circle graphs can have a prepopulated title or can allow the student to populate it. The color of the “wedges” is predetermined by the system.);

• Matching, allows for the use of text or graphics as the matching objects (The student clicks on one object and then clicks on a second object to connect them.);

• Highlighting Text, allows for designated text to be highlighted in a word, phrase, sentence, or paragraph; and the

• Graphic Modification Hot Spot, allows for one image to replace another image when a hot spot is clicked.

Text-Dependent Analysis (TDA) Items

The English Language Arts (ELA) section of the Forward Exam presents students with a Text-Dependent Analysis (TDA) item. A TDA is a text-based analysis based on a single passage or a multiple passage set that each student has read during the assessment. The passage or passage set will consist of either literary or informational text. In order to successfully answer a TDA, students must analyze and use information from the passage(s) to plan a comprehensive, holistic response. Students will then write their response including supporting evidence from the passage(s). Students will have up to 5,000 characters to formulate their response. Students’ responses are scored using a rubric that takes into account both the composition and the conventions of the student’s writing.

The TDA portion of the Forward Exam requires students to read the text and then respond in writing in one of two ways:

• identifying and explaining a theme or central idea, using textual evidence to support the claim about what that theme or central idea is, or

• analyzing the development of an event, character, central ideas, or theme, using textual evidence to support the explanation and analysis.

TDA Item Samplers are available at https://dpi.wi.gov/assessment/forward/sample-items.

https://dpi.wi.gov/assessment/forward/sample-items




Go on to the next page.

MATHEMATICS ITEMS—SESSION 1

Answer the items below.

1 . Demarcus worked on his science project for 3 hours. For how many minutes did he work on his project?

A. 60

B. 63

C. 120

D. 180

2 . The table shows the fraction of each project several students have completed.

StudentMath

ProjectReading Project

Aaron 4 } 5

2 } 8

Bonnie 2 } 5

7 } 8

Cam 4 } 8

4 } 5

Drea 1 } 8

3 } 8

Which student has completed more of his/her math project than his/her reading project?

A. Aaron

B. Bonnie

C. Cam

D. Drea




3 . Catherine is solving the number statement “48 is 6 times as many as __.” What number goes in the blank to solve the number statement?

4 . Percy cuts out a piece of fabric in the shape shown on the grid. He folds the fabric in half so both halves match. Draw a line across the shape to show where Percy folds the fabric.

Percy’s Fabric




5 . What is 3 1 } 4 – 1 2 }

4 ?

A. 1 3 } 4

B. 2 1 } 4

C. 2 3 } 4

D. 4 3 } 4

6 . A protractor is used to measure angle FGH.

10170

2016030150

40140

50130

60120

70110

80100

9010080110

70120

60130

50

140

40

150

30

160

2017

010

180 0 0180

GF

H

What is the measure of angle FGH?

A. 45°

B. 55°

C. 135°

D. 145°


STOP.


7 . Yuri scored 3,670 points in a video game. Amelia scored three thousand seven hundred forty-five points in the same game. Use <, >, or = to compare Yuri’s and Amelia’s scores.

8 . Peter is listing all the factors of 72. Which factor pair should be included on his list?

A. 2 × 70

B. 4 × 18

C. 7 × 9

D. 7 × 12


STOP.



STOP.





Answer the items below.

1 . Several cities recorded the amount of rainfall during a recent rainstorm.

Amount of Rainfall (inches)

0 114

12 1 1

4 1 12

34

What is the total amount of rainfall, in inches, that fell in all of the cities?

A. 1 1 } 4

B. 3 3 } 4

C. 8 3 } 4

D. 15

2 . What is 3,805 – 678?




3 . Julie creates a number pattern that starts with 3 and uses the rule “add 7.” Which statement about Julie’s number pattern is correct?

A. All of the numbers in the pattern will be odd.

B. All of the numbers in the pattern will be even.

C. The numbers in the pattern will alternate between odd and even.

D. The first number in the pattern will be odd but the rest will be even.

4 . Write the sum of 43 } 100

+ 2 } 10

as a fraction.




5 . Which shape has zero lines of symmetry?

A.

B.

C.

D.


STOP.


6 . An angle is shown.

20°x°ray 1

ray 2

ray 3

The measure of the angle formed by ray 1 and ray 3 is 80°.

Use the numbers, variables, and symbols below the blank lines to make an equation that could be used to find the value of x.

_____ _____ _____ = _____0 + 0 0

20 - 20 2080 × 80 80x ÷ x x

7 . Jackson’s hometown has a population of 145,289. What is the population of Jackson’s hometown when rounded to the nearest thousand?

A. 145,000

B. 145,300

C. 146,000

D. 150,000


STOP.



STOP.



MATHEMATICS—APPENDIX

SUMMARY DATA

Grade 4

Sample Number

AlignmentAnswer

KeyDepth of

KnowledgeAnnotations

Session 1

1 4.MD.1 D 2 The question asks the student to convert hours to minutes.

A. Incorrect. The student uses the number of minutes in 1 hour.

B. Incorrect. The student adds 60 plus 3.

C. Incorrect. The student uses the number of minutes in 2 hours.

D. Correct. The student multiplies 60 times 3.

2 4.NF.2 A 2 The question asks the student to compare fractions with like and unlike denominators.

A. Correct. The student compares 4 } 5

and

2 } 8 to 1 }

2 .

B. Incorrect. The student thinks the larger fraction has fewer parts of the whole.

C. Incorrect. The student thinks the larger fraction has more parts of the whole.

D. Incorrect. The student uses a greater fraction for the reading project than the math project.

3 4.OA.1 Exemplar:

8

1 The question asks the student to find the missing number in a verbal statement.

To receive full credit, the student must enter 8 or an equivalent value.

4 4.G.3 See Annotations

1 The question asks the student to create a line of symmetry.

To receive full credit, the student must draw a line down the center of the figure.



Grade 4

Sample Number

AlignmentAnswer

KeyDepth of


5 4.NF.3c A 1 The question asks the student to subtract mixed numbers.

A. Correct. The student subtracts

13 } 4 minus 6 }

4 and converts the difference

to a mixed number.

B. Incorrect. The student subtracts the whole numbers and then subtracts the fractions backwards.

C. Incorrect. The student does not subtract from the whole number when borrowing.

D. Incorrect. The student adds the fractions.

6 4.MD.6 C 1 The question asks the student to use a protractor to measure an angle.

A. Incorrect. The student reads the protractor from right to left and adds 5 to 40.

B. Incorrect. The student reads the protractor from right to left and adds 5 to 50.

C. Correct. The student reads the protractor from left to right.

D. Incorrect. The student reads the protractor from left to right and adds 5 to 140.

7 4.NBT.2 3670 < 3745

or

3745 > 3670

1 The question asks the student to compare two numbers.

To receive full credit, the student must enter 3670 < 3745 or 3745 > 3670.



Grade 4

Sample Number

AlignmentAnswer

KeyDepth of


8 4.OA.4 B 1 The question asks the student to find factors of a number.

A. Incorrect. The student adds 70 and 2 to get 72.

B. Correct. The student multiplies 4 and 18 to get 72.

C. Incorrect. The student incorrectly multiplies 7 and 9.

D. Incorrect. The student multiplies 7 and 10 to get 70, and adds 2 from the 12.



Grade 4

Sample Number

AlignmentAnswer

KeyDepth of


Session 2

1 4.MD.4 C 2 The question asks the student to use information from a line plot.

A. Incorrect. The student adds the column with the greatest number of marks.

B. Incorrect. The student adds

1 } 4 + 1 }

2 + 3 }

4 + 1 + 1 1 }

4 .

C. Correct. The student adds all the amounts of rainfall from the line plot.

D. Incorrect. The student uses the number of cities that were recorded in the line plot.

2 4.NBT.4 Exemplar:

3127

1 The question asks the student to subtract two numbers.

To receive full credit, the student must enter 3127 or an equivalent value.

3 4.OA.5 C 2 The question asks the student to use a rule for a number pattern.

A. Incorrect. The student uses odd numbers only.

B. Incorrect. The student uses the two odd numbers to create an even number and applies the observation to the entire pattern.

C. Correct. The student observes the pattern 3, 10, 17, 24, …

D. Incorrect. The student uses the second number in the pattern as the observation for the entire pattern.



Grade 4

Sample Number

AlignmentAnswer

KeyDepth of


4 4.NF.5 Exemplar:

63 } 100

1 The question asks the student to add two fractions with unlike denominators.

To receive full credit, the student must

enter 63 } 100

or an equivalent fraction.

5 4.G.3 B 1 The question asks the student to identify a shape with no lines of symmetry.

A. Incorrect. The student assumes shapes with diagonal sides have no lines of symmetry.

B. Correct. The student understands the shape does not have a line of symmetry.

C. Incorrect. The student does not see the horizontal line of symmetry.

D. Incorrect. The student thinks the shape has too many sides to be able to have any lines of symmetry.

6 4.MD.7 Exemplar:

20 + x = 80

2 The question asks the student to create an equation that can be used to find the value of x.

To receive full credit, the student must create the equation 20 + x = 80 (or an equivalent equation).

7 4.NBT.3 A 1 The question asks the student to round a number to the nearest thousands place.

A. Correct. The student rounds down to the nearest thousands place.

B. Incorrect. The student rounds up to the nearest hundreds place.

C. Incorrect. The student rounds up to the nearest thousands place.

D. Incorrect. The student rounds up to the nearest ten thousands place.



Copyright © 2017 by the Wisconsin Department of Public Instruction. The materials contained in this publication may be duplicated by Wisconsin educators for local classroom use. This permission does not extend to the duplication of materials for commercial use.

MathematicsItem Sampler

Grade 4

Documents

Mathematics Item Sampler Grade 4 - dpi.wi.gov · PDF fileGrade 4 Mathematics Item Sampler iv ... This document contains samples of test items similar to those on the Wisconsin Forward